Gene-regulation functions. (A) A gene-regulation function describes how trans inputs, such as transcription factors (I₁, I₂, … I_n), and cis inputs, such as regulatory elements, are transformed into a gene's mRNA level (O). (B) Different functions describe distinct scenarios, using distinct mathematical approaches. Most small-scale approaches rely on a thermodynamically motivated model (i), which explains the dependency on a single tunable trans input and fits the response to a Hill function. The extracted Hill parameters, maximum expression level (M), threshold (T), and sensitivity (n), become functions of the remaining trans- and cis-input variables. Large-scale approaches utilize a host of approaches. (ii) Linear models assume that the output is a linear combination of the cis or trans inputs. (iii) Bayesian networks give the probability distribution of the output given the input values. (iv) Logical (Boolean) circuits consider the output as a result of applying logical operations on the inputs. (Top) The assumption underlying each modeling approach; (middle) the gene-regulation function in this modeling approach; and (bottom) an equivalent mathematical formulation. All modeling approaches are applicable in both small- and large-scale studies.